Question

Using the identity sin? O + cos? O = 1, find the value of tan O, to the nearest

hundredth, if sin 0 = 0.27 and 0 < 0 < 7

Answer 1

3.7

Explanation:

Given

• sin²θ + cos²θ = 1
• sinθ = 0.27

Solving for cosθ

• cos²θ = 1 - sin²θ
• cos²θ = 1 - (0.27)²
• cos²θ = 0.0729

Finding tanθ

• tanθ = sinθ / cosθ
• tanθ = 0.27 / 0.0729
• tanθ = 3.7

Verifying it lies in the range

• θ = tan⁻¹ (3.7)
• θ = 74.88°
• Range is : 0 < θ < π/2 [or 0 < θ < 90°]
• It lies in the range [Verified]